2008/11/26 by Alain Sarlette, Rodolphe Sepulchre, Sarlette, Alain +1 · 6 citations
Computer Science · Mathematics · #Differential Geometry (math.DG) #Distributed Control Multi-Agent Systems #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.0811.4275
openalex publication_date 2008/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e. maximizing the consensus) or balance (i.e. minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO(n) and the Grassmann manifold Gr(p,n) are treated as original examples. A link is also drawn with the many existing results on the circle.